Question

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=2, what is the area of the shaded region? Answer as a decimal, if necessary. Little confused on this one.

Answer 1

10 units²

Explanation:

Consider the unshaded region to consists of 2 triangles, ∆AED and ∆BEC, which are both of equal dimensions. Their bases and heights are both the same. Both triangles are embedded inside a rectangle ABCD.

Area of the shaded region = Area of rectangle - area of the 2 triangles.

Area of rectangle = l*w

l = 10

w = 2

`Area_R = 10*2 = 20 units^2`

Area of the 2 triangles = 2(½*b*h)

b = 2

h = 5

`Area_T = 2((1)/(2)*2*5)`

`Area_T = 1*2*5 = 10 units^2`

Area of shaded region = 20 - 10 = 10 units²